Yes. All buttons with the exception of the PS button (the button with the Playstation logo on it) will be functional when connected to a PS3. Your Options button basically becomes the Start button.
However, there do exist some PS3 games for which a PS4 controller will not work. To find out which ones they are, it's basically a process of trial and error.
However, there do exist some PS3 games for which a PS4 controller will not work. To find out which ones they are, it's basically a process of trial and error.
To my understanding the PS3 recognizes the Dualshock 4 as a generic PC controller. That's obviously a problem for games with heavy emphasis on pressure sensitivity like Gran Turismo, but it should be serviceable for any fighting games.
Only saying this to stress that it's more a case of how practical it is for some games more than others, not so much "it works or it doesn't". I can't think of one that wouldn't at least detect it.